> On 5 Sep 2019, at 01:12, 'Brent Meeker' via Everything List > <[email protected]> wrote: > > > > On 9/4/2019 8:39 AM, Bruno Marchal wrote: >>> On 2 Sep 2019, at 22:31, 'Brent Meeker' via Everything List >>> <[email protected]> wrote: >>> >>> >>> >>> On 9/2/2019 8:57 AM, Bruno Marchal wrote: >>>> Indeed that can be said illustrated from the fact that in string theory, >>>> to get the mass of the photon right, we use 1+2+3+4+5+… = -1/12, which is >>>> a statement about the prime numbers, just a little bit disguised >>> I'm sure you know that equation depends on assumptions about how limits are >>> to be taken. >> >> Of course. That is the most axing part: that we need to invoque the prime >> numbers, or equivalently the zeta function, to get a reasonable account of >> why it make sense to say that the sum on all natural numbers is -1/12. >> Now this “zeta-regularisation” has become common. To justify the mass of the >> photon, the string theorits needs sophisticated tools (yet still essentially >> arithmetical) from Number theory. > > But it takes a redefinition of what one means by "convergence”.
Yes. That is the point. We redefine all terms, all the times, when we do science. Bruno > There's a good explanation here: > https://www.quora.com/Whats-the-intuition-behind-the-equation-1+2+3+-cdots-tfrac-1-12 > > Brent > >> >> It is essentially arithmetical by the fact that despite its use of complex >> analysis in its most common formulation, the Riemann Hypothesis (Conjecture >> RH) is an arithmetical sentence, indeed a pi_1 (the negation of a sigma_1 >> sentences). >> >> If the RH is false, then even the tiny Robinson Arithmetic, which cannot >> even prove that for all x 0 + x = x, is able to refute RH. That has been >> shown by Turing: if a non trivial zero of zeta is not on the critical line, >> a machine can find it. The existence of such zero is of >> (Post-Kleene)-complexity equal to “sigma_1". >> >> Bruno >> >> >>> Brent >>> >>> -- >>> You received this message because you are subscribed to the Google Groups >>> "Everything List" group. >>> To unsubscribe from this group and stop receiving emails from it, send an >>> email to [email protected]. >>> To view this discussion on the web visit >>> https://groups.google.com/d/msgid/everything-list/584572cc-75e9-ca69-303f-1a9f907f1601%40verizon.net. > > > -- > You received this message because you are subscribed to the Google Groups > "Everything List" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected]. > To view this discussion on the web visit > https://groups.google.com/d/msgid/everything-list/653597f4-6b48-e90c-d256-33378ada95dd%40verizon.net. -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/F6BC2027-D3FD-40ED-8FFE-972C75EAF91B%40ulb.ac.be.
